Related papers: Accelerating the DC algorithm for smooth functions
This paper proposes a novel Difference-of-Convex (DC) decomposition for polynomials using a power-sum representation, achieved by solving a sparse linear system. We introduce the Boosted DCA with Exact Line Search (BDCAe) for addressing…
This paper presents an algorithm for approximately minimizing a convex function in simple, not necessarily bounded convex domains, assuming only that function values and subgradients are available. No global information about the objective…
When solving decision-making problems with mathematical optimization, some constraints or objectives may lack analytic expressions but can be approximated from data. When an approximation is made by neural networks, the underlying problem…
In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous…
Novel coordinate descent (CD) methods are proposed for minimizing nonconvex functions consisting of three terms: (i) a continuously differentiable term, (ii) a simple convex term, and (iii) a concave and continuous term. First, by extending…
A sequential quadratic programming (SQP) algorithm is designed for nonsmooth optimization problems with upper-C^2 objective functions. Upper-C^2 functions are locally equivalent to difference-of-convex (DC) functions with smooth convex…
In two earlier papers, we designed a distributed deterministic asynchronous algorithm for minimizing the sum of subdifferentiable and proximable functions and a regularizing quadratic on time-varying graphs based on Dykstra's algorithm, or…
In this paper we introduce a novel abstract descent scheme suited for the minimization of proper and lower semicontinuous functions. The proposed abstract scheme generalizes a set of properties that are crucial for the convergence of…
In this paper, we consider smooth convex optimization problems with simple constraints and inexactness in the oracle information such as value, partial or directional derivatives of the objective function. We introduce a unifying framework,…
Distributed optimization often requires finding the minimum of a global objective function written as a sum of local functions. A group of agents work collectively to minimize the global function. We study a continuous-time decentralized…
In this paper, we study the problem of minimizing a sum of smooth and strongly convex functions split over the nodes of a network in a decentralized fashion. We propose the algorithm $ESDACD$, a decentralized accelerated algorithm that only…
In order to solve the minimization of a nonsmooth convex function, we design an inertial second-order dynamic algorithm, which is obtained by approximating the nonsmooth function by a class of smooth functions. By studying the asymptotic…
In this paper, we develop a new computational approach which is based on minimizing the difference of two convex functionals (DC) to solve a broader class of phase retrieval problems. The approach splits a standard nonlinear least squares…
Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…
We consider distributed optimization with smooth convex objective functions defined on an undirected connected graph. Inspired by mirror descent mehod and RLC circuits, we propose a novel distributed mirror descent method. Compared with…
Distributed consensus optimization has received considerable attention in recent years; several distributed consensus-based algorithms have been proposed for (nonsmooth) convex and (smooth) nonconvex objective functions. However, the…
We develop new sub-optimality bounds for gradient descent (GD) that depend on the conditioning of the objective along the path of optimization rather than on global, worst-case constants. Key to our proofs is directional smoothness, a…
We study the convergence issue for inexact descent algorithm (employing general step sizes) for multiobjective optimizations on general Riemannian manifolds (without curvature constraints). Under the assumption of the local…
In this paper, we focus on the decentralized composite optimization for convex functions. Because of advantages such as robust to the network and no communication bottle-neck in the central server, the decentralized optimization has…
We study the worst-case behavior of Block Coordinate Descent (BCD) type algorithms for unconstrained minimization of coordinate-wise smooth convex functions. This behavior is indeed not completely understood, and the practical success of…